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Seminários do IMPA

Hammersley’s Last-Passage Percolation (LPP) can be described as follows: let points be taken uniformly and independently in the square $[0,1]^2$, then what is the maximal number of points that can be visited by an up-right path? In this talk, I will introduce a generalization of this problem, where the up-right condition is replaced by a global condition on the path. There are only very few results for this LPP with constraint, but they already have nice applications, in particular in the context of directed polymers in random environment.